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Consider the rectangle: 4V20 + 2V24 3V8
Select all expressions that are equivalent to the perimeter of the rectangle.
HELP ASAP PLZ.​

Consider The Rectangle 4V20 2V24 3V8 Select All Expressions That Are Equivalent To The Perimeter Of The RectangleHELP ASAP PLZ class=

Sagot :

MrRoyal

The perimeter of a rectangle is the sum of visible lengths of the rectangle. The equivalent expressions are:

[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]

[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]

[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]

Given that:

[tex]L = 4\sqrt{20} + 2\sqrt{24}[/tex] --- Length

[tex]W = 3\sqrt 8[/tex] --- Width

The perimeter (P) of the rectangle is:

[tex]P = 2 \times (L + W)[/tex]

So, we have:

[tex]P = 2 \times (4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]

[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]

Rewrite as:

[tex]P = 2( 3\sqrt 8+4\sqrt{20} + 2\sqrt{24})[/tex]

Expand

[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]

Further expand

[tex]P = 6\sqrt 8 +8\sqrt{20} + 2\sqrt{24}[/tex]

[tex]P = 6\sqrt{4\times 2} +8\sqrt{4\times 5} + 2\sqrt{4\times 6}[/tex]

Evaluate square roots

[tex]P = 6 \times 2\sqrt{2} +8\times 2\sqrt{5} + 2\times 2\sqrt{6}[/tex]

[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]

Hence, the equivalent expressions are:

[tex]P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)[/tex]

[tex]P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})[/tex]

[tex]P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}[/tex]

Read more about perimeters at:

https://brainly.com/question/6465134

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